1. Field of the Invention
The invention relates to a procedure for determining a high-reflection gem cut, procedure for cutting a high-reflection gem, and a cut gem of high reflection.
2. Description of the Related Art
The reflection or light efficiency of a gem cut essentially depends on the dimension and number of facets and on the angles created by them. Many trials have been carried out in the past for improving gem cuts used in practice or for creating new gem cuts. These trials are based, on the one hand, on empirical cutting trials, or [on the other hand] on simple calculations which also take into account the optical refraction of the raw material to be cut.
For example, DE-AS 1 557 652 specifies combinations of upper part (crown) principal facet angles and lower part (pavilion) principal facet angles for various types of minerals, for example 27xc2x0/36xc2x0 for diamonds, 25xc2x0/49xc2x0 for quartz, 24xc2x0/45xc2x0 for tourmaline, 29xc2x0/38xc2x0 for garnet, 28xc2x0/39xc2x0 for beryl, and 28xc2x0/39xc2x0 for corundum.
All these angle combinations have in common the fact that the lower part (pavilion) principal facet angle is larger than the upper part (crown) principal facet angle.
Such cuts, especially for diamonds, with angle combinations of 24.5xc2x0/39.5xc2x0, or of 33.5xc2x0/41.5xc2x0 are also known from DE 42 10 995 A1.
It has been proved in practice that the angle combinations mentioned in the literature for gem cutting do not yet produce maximum light efficiency, and that a systematic specification of optimal angle combinations is very desirable for all materials to be cut, which have different optical refraction.
Therefore, the objective of the invention is to specify a procedure for determining a gem cut, a procedure for gem cutting and a cut gem, whereby optimal light efficiency should be achieved when applying the specified angle values, while talking into consideration the light refraction of the material to be cut.
This objective is solved by a cut gem with characteristics including high reflection with at least three principal pavilion facets and at least three principal crown facets, the angle between the principal pavilion facets and the girdle surface being greater than the angle between the principal crown facets and the girdle surface. At angle 0xc2x0 a table is formed instead of the principal crown facets, with principal pavilion facet angle (UHFW) ranging between 41xc2x0 and 46xc2x0. Principal crown facet angle (OHFW) corresponds to an angle selected from a group of predetermined, preferred angles, which are subject to mean optical refraction n ranging between 1.50 and 3.00 of the raw material to be cut, and principal pavilion facet angle (UHFW). The group of predetermined, preferred angles includes the following angles:
at n 1.50 and UHFW of 42xc2x0angles of 13xc2x0 to 33xc2x0
at n 1.50 and UHFW of 43xc2x0angles of 60xc2x0 to 26xc2x0
at n 1.50 and UHFW of 44xc2x0angles of 1xc2x0 to 18xc2x0
at n 1.50 and UHFW of 45xc2x0angles of 0xc2x0 to 9xc2x0
at n 1.50 and UHFW of 46xc2x0angles of 0xc2x0
at n 1.55 and UHFW of 41xc2x0angles of 18xc2x0 to 33xc2x0
at n 1.55 and UHFW of 42xc2x0angles of 12xc2x0 to 30xc2x0
at n 1.55 and UHFW of 43xc2x0angles of 6xc2x0 to 26xc2x0
at n 1.55 and UHFW of 44xc2x0angles of 1xc2x0 to 18xc2x0
at n 1.55 and UHFW of 45xc2x0angles of 0xc2x0 to 13xc2x0
at n 1.55 and UHFW of 46xc2x0angles of 0xc2x0 to 5xc2x0
at n 1.60 and UHFW of 41xc2x0angles of 17xc2x0 to 31xc2x0
at n 1.60 and UHFW of 42xc2x0angles of 11xc2x0 to 28xc2x0
at n 1.60 and UHFW of 43xc2x0angles of 6xc2x0 to 23xc2x0
at n 1.60 and UHFW of 44xc2x0angles of 1xc2x0 to 20xc2x0
at n 1.60 and UHFW of 45xc2x0angles of 0xc2x0 to 14xc2x0
at n 1.60 and UHFW of 46xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.65 and UHFW of 41xc2x0angles of 16xc2x0 to 28xc2x0
at n 1.65 and UHFW of 42xc2x0angles of 11xc2x0 to 25xc2x0
at n 1.65 and UHFW of 43xc2x0angles of 5xc2x0 to 21xc2x0
at n 1.65 and UHFW of 44xc2x0angles of 1to 17xc2x0
at n 1.65 and UHFW of 45xc2x0angles of 0xc2x0 to 14xc2x0
at n 1.65 and UHFW of 46xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.70 and UHFW of 41xc2x0angles of 15xc2x0 to 27xc2x0
at n 1.70 and UHFW of 42xc2x0angles of 10xc2x0 to 23xc2x0
at n 1.70 and UHFW of 43xc2x0angles of 5xc2x0 to 20xc2x0
at n 1.70 and UHFW of 44xc2x0angles of 1xc2x0 to 17xc2x0
at n 1.70 and UHFW of 45xc2x0angles of 0xc2x0 to 12xc2x0
at n 1.70 and UHFW of 46xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.75 and UHFW of 41xc2x0angles of 15xc2x0 to 25xc2x0
at n 1.75 and UHFW of 42xc2x0angles of 10xc2x0 to 22xc2x0
at n 1.75 and UHFW of 43xc2x0angles of 5xc2x0 to 19xc2x0
at n 1.75 and UHFW of 44xc2x0angles of 1xc2x0 to 15xc2x0
at n 1.75 and UHFW of 45xc2x0angles of 0xc2x0 to 12xc2x0
at n 1.75 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 1.80 and UHFW of 41xc2x0angles of 14xc2x0 to 24xc2x0
at n 1.80 and UHFW of 42xc2x0angles of 10xc2x0 to 21xc2x0
at n 1.80 and UHFW of 43xc2x0angles of 5xc2x0 to 19xc2x0
at n 1.80 and UHFW of 44xc2x0angles of 1xc2x0 to 14xc2x0
at n 1.80 and UHFW of 45xc2x0angles of 0xc2x00 to 11xc2x0
at n 1.80 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 1.85 and UHFW of 41xc2x0angles of 14xc2x0 to 23xc2x0
at n 1.85 and UHFW of 42xc2x0angles of 9xc2x0 to 20xc2x0
at n 1.85 and UHFW of 43xc2x0angles of 5xc2x0 to 17xc2x0
at n 1.85 and UHFW of 44xc2x0angles of 1xc2x0 to 14xc2x0
at n 1.85 and UHFW of 45xc2x0angles of 0xc2x0 to 11xc2x0
at n 1.85 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 1.90 and UHFW of 41xc2x0angles of 14xc2x0 to 22xc2x0
at n 1.90 and UHFW of 42xc2x0angles of 9xc2x0 to 20xc2x0
at n 1.90 and UHFW of 43xc2x0angles of 5xc2x0 to 17xc2x0
at n 1.90 and UHFW of 44xc2x0angles of 1xc2x0 to 14xc2x0
at n 1.90 and UHFW of 45xc2x0angles of 0xc2x0 to 9xc2x0
at n 1.90 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 1.95 and UHFW of 46xc2x0angles of 13xc2x0 to 22xc2x0
at n 1.95 and UHFW of 42xc2x0angles of 9xc2x0 to 20xc2x0
at n 1.95 and UHFW of 43xc2x0angles of 5xc2x0 to 16xc2x0
at n 1.95 and UHFW of 44xc2x0angles of 1xc2x0 to 13xc2x0
at n 1.95 and UHFW of 45xc2x0angles of 0xc2x0 to 9xc2x0
at n 1.95 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.00 and UHFW of 41xc2x0angles of 13xc2x0 to 22xc2x0
at n 2.00 and UHFW of 42xc2x0angles of 8xc2x0 to 17xc2x0
at n 2.00 and UHFW of 43xc2x0angles of 4xc2x0 to 16xc2x0
at n 2.00 and UHFW of 44xc2x0angles of 1xc2x0 to 12xc2x0
at n 2.00 and UHFW of 45xc2x0angles of 0xc2x0 to 9xc2x0
at n 2.00 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.05 and UHFW of 41xc2x0angles of 13xc2x0 to 19xc2x0
at n 2.05 and UHFW of 42xc2x0angles of 8xc2x0 to 16xc2x0
at n 2.05 and UHFW of 43xc2x0angles of 4xc2x0 to 14xc2x0
at n 2.05 and UHFW of 44xc2x0angles of 1xc2x0 to 12xc2x0
at n 2.05 and UHFW of 45xc2x0angles of 0xc2x0 to 9xc2x0
at n 2.05 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.10 and UHFW of 41xc2x0angles of 12xc2x0 to 19xc2x0
at n 2.10 and UHFW of 42xc2x0angles of 8xc2x0 to 16xc2x0
at n 2.10 and UHFW of 43xc2x0angles of 4xc2x0 to 14xc2x0
at n 2.10 and UHFW of 44xc2x0angles of 1xc2x0 to 12xc2x0
at n 2.10 and UHFW of 45xc2x0angles of 0xc2x0 to 8xc2x0
at n 2.10 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.15 and UHFW of 41xc2x0angles of 12xc2x0 to 18xc2x0
at n 2.15 and UHFW of 42xc2x0angles of 8xc2x0 to 16xc2x0
at n 2.15 and UHFW of 43xc2x0angles of 4xc2x0 to 14xc2x0
at n 2.15 and UHFW of 44xc2x0angles of 1xc2x0 to 11xc2x0
at n 2.15 and UHEW of 45xc2x0angles of 0xc2x0 to 8xc2x0
at n 2.15 and UHEW of 46xc2x0angles of 0xc2x0 to 4xc2x0
at n 2.15 and UHFW of 41xc2x0angles of 12xc2x0 to 17xc2x0
at n 2.20 and UHFW of 42xc2x0angles of 8xc2x0 to 15xc2x0
at n 2.20 and UHFW of 43xc2x0angles of 4xc2x0 to 13xc2x0
at n 2.20 and UHFW of 44xc2x0angles of 1xc2x0 to 10xc2x0
at n 2.20 and UHFW of 45xc2x0angles of 0xc2x0 to 8xc2x0
at n 2.20 and UHFW of 46xc2x0angles of 0xc2x0 to 4xc2x0
at n 2.20 and UHFW of 41xc2x0angles of 12xc2x0 to 17xc2x0
at n 2.25 and UHFW of 42xc2x0angles of 8xc2x0 to 15xc2x0
at n 2.25 and UHFW of 43xc2x0angles of 4xc2x0 to 13xc2x0
at n 2.25 and UHFW of 44xc2x0angles of 1xc2x0 to 10xc2x0
at n 2.25 and UHFW of 45xc2x0angles of 0xc2x0 to 8xc2x0
at n 2.25 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.30 and UHFW of 41xc2x0angles of 12xc2x0 to 17xc2x0
at n 2.30 and UHFW of 42xc2x0angles of 7xc2x0 to 15xc2x0
at n 2.30 and UHFW of 43xc2x0angles of 4xc2x0 to 13xc2x0
at n 2.30 and UHFW of 44xc2x0angles of 1xc2x0 to 10xc2x0
at n 2.30 and UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
at n 2.30 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.35 and UHFW of 41xc2x0angles of 11xc2x0 to 17xc2x0
at n 2.35 and UHFW of 42xc2x0angles of 7xc2x0 to 14xc2x0
at n 2.35 and UHFW of 43xc2x0angles of 4xc2x0 to 12xc2x0
at n 2.35 and UHFW of 44xc2x0angles of 1xc2x0 to 10xc2x0
at n 2.35 and UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
at n 2.35 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.40 and UHFW of 41xc2x0angles of 11xc2x0 to 16xc2x0
at n 2.40 and UHFW of 42xc2x0angles of 7xc2x0 to 14xc2x0
at n 2.40 and UHFW of 43xc2x0angles of 4xc2x0 to 12xc2x0
at n 2.40 and UHFW of 44xc2x0angles of 1xc2x0 to 10xc2x0
at n 2.40 and UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
at n 2.40 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.45 and UHFW of 41xc2x0angles of 11xc2x0 to 16xc2x0
at n 2.45 and UHEW of 42xc2x0angles of 7xc2x0 to 14xc2x0
at n 2.45 and UHFW of 43xc2x0angles of 4xc2x0 to 12xc2x0
at n 2.45 and UHFW of 44xc2x0angles of 1xc2x0 to 1xc2x0
at n 2.45 and UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
at n 2.45 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.50 and UHFW of 41xc2x0angles of 11xc2x0 to 16xc2x0
at n 2.50 and UHFW of 42xc2x0angles of 7xc2x0 to 14xc2x0
at n 2.50 and UHFW of 43xc2x0angles of 4xc2x0 to 11xc2x0
at n 2.50 and UHFW of 44xc2x0angles of 1xc2x0 to 9xc2x0
at n 2.50 and UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
at n 2.50 and UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.55 and UHFW of 41xc2x0angles of 11xc2x0 to 15xc2x0
at n 2.55 and UHFW of 42xc2x0angles of 7xc2x0 to 13xc2x0
at n 2.55 and UHFW of 43xc2x0angles of 4xc2x0 to 11xc2x0
at n 2.55 and UHFW of 44xc2x0angles of 1xc2x0 to 9xc2x0
at n 2.55 and UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
at n 2.55 and UHFW of 46xc2x0angles of 0xc2x0 to 2xc2x0
at n 2.60 and UHFW of 41xc2x0angles of 11xc2x0 to 15xc2x0
at n 2.60 and UHFW of 42xc2x0angles of 7xc2x0 to 13xc2x0
at n 2.60 and UHFW of 43xc2x0angles of 4xc2x0 to 11xc2x0
at n 2.60 and UHFW of 44xc2x0angles of 1xc2x0 to 9xc2x0
at n 2.60 and UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
at n 2.60 and UHFW of 46xc2x0angles of 0xc2x0 to 2xc2x0
at n 2.65 and UHFW of 41xc2x0angles of 10xc2x0 to 15xc2x0
at n 2.65 and UHFW of 42xc2x0angles of 7xc2x0 to 13xc2x0
at n 2.65 and UHFW of 43xc2x0angles of 4xc2x0 to 11xc2x0
at n 2.65 and UHFW of 44xc2x0angles of 1xc2x0 to 9xc2x0
at n 2.65 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.65 and UHFW of 46xc2x0angles of 0xc2x0 to 2xc2x0
at n 2.70 and UHFW of 41xc2x0angles of 10xc2x0 to 15xc2x0
at n 2.70 and UHFW of 42xc2x0angles of 7xc2x0 to 13xc2x0
at n 2.70 and UHFW of 43xc2x0angles of 4xc2x0 to 11xc2x0
at n 2.70 and UHFW of 44xc2x0angles of 1xc2x0 to 9xc2x0
at n 2.70 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.70 and UHFW of 46xc2x0angles of 0xc2x0 to 2xc2x0
at n 2.75 and UHFW of 41xc2x0angles of 10xc2x0 to 15xc2x0
at n 2.75 and UHFW of 42xc2x0angles of 7xc2x0 to 12xc2x0
at n 2.75 and UHFW of 43xc2x0angles of 4xc2x0 to 11xc2x0
at n 2.75 and UHFW of 44xc2x0angles of 1xc2x0 to 9xc2x0
at n 2.75 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.75 and UHFW of 46xc2x0angles of 0xc2x0 to 1xc2x0
at n 2.80 and UHFW of 41xc2x0angles of 10xc2x0 to 15xc2x0
at n 2.80 and UHFW of 42xc2x0angles of 7xc2x0 to 12xc2x0
at n 2.80 and UHFW of 43xc2x0angles of 4xc2x0 to 10xc2x0
at n 2.80 and UHFW of 44xc2x0angles of 1xc2x0 to 8xc2x0
at n 2.80 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.80 and UHFW of 46xc2x0angles of 0xc2x0 to 1xc2x0
at n 2.85 and UHFW of 41xc2x0angles of 10xc2x0 to 14xc2x0
at n 2.85 and UHFW of 42xc2x0angles of 7xc2x0 to 12xc2x0
at n 2.85 and UHFW of 43xc2x0angles of 4xc2x0 to 10xc2x0
at n 2.85 and UHFW of 44xc2x0angles of 1xc2x0 to 8xc2x0
at n 2.85 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.85 and UHFW of 46xc2x0angles of 0xc2x0 to 1xc2x0
at n 2.90 and UHFW of 41xc2x0angles of 10xc2x0 to 14xc2x0
at n 2.90 and UHFW of 42xc2x0angles of 7xc2x0 to 12xc2x0
at n 2.90 and UHFW of 43xc2x0angles of 4xc2x0 to 10xc2x0
at n 2.90 and UHFW of 44xc2x0angles of 1xc2x0 to 8xc2x0
at n 2.90 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.90 and UHFW of 46xc2x0angles of 0xc2x0 to 1xc2x0
at n 2.95 and UHFW of 41xc2x0angles of 10xc2x0 to 14xc2x0
at n 2.95 and UHFW of 42xc2x0angles of 7xc2x0 to 12xc2x0
at n 2.95 and UHFW of 43xc2x0angles of 4xc2x0 to 10xc2x0
at n 2.95 and UHFW of 44xc2x0angles of 10xc2x0 to 8xc2x0
at n 2.95 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.95 and UHFW of 46xc2x0angles of 0xc2x0 to 1xc2x0
at n 3.00 and UHFW of 41xc2x0angles of 10xc2x0 to 14xc2x0
at n 3.00 and UHFW of 42xc2x0angles of 7xc2x0 to 12xc2x0
at n 3.00 and UHFW of 43xc2x0angles of 4xc2x0 to 10xc2x0
at n 3.00 and UHFW of 44xc2x0angles of 1xc2x0 to 8xc2x0
at n 3.00 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 3.00 and UHFW of 46xc2x0angles of 0xc2x0 to 1xc2x0
Principal crown facet angles (OHFW) for values of n and principal pavilion facet angles (UHFW) not specifically specified above may be interpolated from the above specified values. Within the group of angles just specified, a group of especially preferred angles includes:
at n 1.50 and UHFW of 42xc2x0angles of 16xc2x0 to to 25xc2x0
at n 1.50 and UHFW of 43xc2x0angles of 10xc2x0 to 21xc2x0
at n 1.50 and UHFW of 44xc2x0angles of 3xc2x0 to 16xc2x0
at n 1.50 and UHFW of 45xc2x0angles of 0xc2x0 to 9xc2x0
at n 1.55 and UHFW of 41xc2x0angles of 20xc2x0 to 26xc2x0
at n 1.55 and UHFW of 42xc2x0angles of 15xc2x0 to 23xc2x0
at n 1.55 and UHFW of 43xc2x0angles of 9xc2x0 to 19xc2x0
at n 1.55 and UHFW of 44xc2x0angles of 3xc2x0 to 16xc2x0
at n 1.55 and UHFW of 45xc2x0angles of 0xc2x0 to 8xc2x0
at n 1.60 and UHFW of 41xc2x0angles of 19xc2x0 to 25xc2x0
at n 1.60 and UHFW of 42xc2x0angles of 14xc2x0 to 21xc2x0
at n 1.60 and UHFW of 43xc2x0angles of 8xc2x0 to 17xc2x0
at n 1.60 and UHFW of 44xc2x0angles of 2xc2x0 to 12xc2x0
at n 1.60 and UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
at n 1.60 and UHFW of 46xc2x0angles of 0xc2x0
at n 1.65 and UHFW of 41xc2x0angles of 19xc2x0 to 23xc2x0
at n 1.65 and UHFW of 42xc2x0angles of 13xc2x0 to 20xc2x0
at n 1.65 and UHFW of 43xc2x0angles of 8xc2x0 to 15xc2x0
at n 1.65 and UHFW of 44xc2x0angles of 2xc2x0 to 11xc2x0
at n 1.65 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.65 and UHFW of 46xc2x0angles of 0xc2x0
at n 1.70 and UHFW of 41xc2x0angles of 18xc2x0 xc2x0 0 to 21xc2x0
at n 1.70 and UHFW of 42xc2x0angles of 120 to 18xc2x0
at n 1.70 and UHFW of 43xc2x0angles of 70 to 14xc2x0
at n 1.70 and UHFW of 44xc2x0angles of 2xc2x0 to 11xc2x0
at n 1.70 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.70 and UHFW of 46xc2x0angles of 0xc2x0
at n 1.75 and UHFW of 41xc2x0angles of 170 to 21xc2x0
at n 1.75 and UHFW of 42xc2x0angles of 120 to 16xc2x0
at n 1.75 and UHFW of 43xc2x0angles of 70 to 13xc2x0
at n 1.75 and UHFW of 44xc2x0angles of 20 to 11xc2x0
at n 1.75 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.75 and UHFW of 46xc2x0angles of 0xc2x0 to 1xc2x0
at n 1.80 and UHFW of 41xc2x0angles of 160 to 19xc2x0
at n 1.80 and UHFW of 42xc2x0angles of 120 to 16xc2x0
at n 1.80 and UHFW of 43xc2x0angles of 70 to 13xc2x0
at n 1.80 and UHFW of 44xc2x0angles of 20 to 10xc2x0
at n 1.80 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.80 and UHFW of 46xc2x0angles of 0xc2x0 to 1xc2x0
at n 1.85 and UHFW of 41xc2x0angles of 16xc2x0 to 18xc2x0
at n 1.85 and UHFW of 42xc2x0angles of 110 to 15xc2x0
at n 1.85 and UHFW of 43xc2x0angles of 60 to 12xc2x0
at n 1.85 and UHFW of 44xc2x0angles of 20 to 10xc2x0
at n 1.85 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.85 and UHFW of 46xc2x0angles of 0xc2x0
at n 1.90 and UHFW of 41xc2x0angles of 160 to 18xc2x0
at n 1.90 and UHFW of 42xc2x0angles of 110 to 14xc2x0
at n 1.90 and UHFW of 43xc2x0angles of 60 to 12xc2x0
at n 1.90 and UHFW of 44xc2x0angles of 20 to 9xc2x0
at n 1.90 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.90 and UHFW of 46xc2x0angles of 0xc2x0
at n 1.95 and UHFW of 41xc2x0angles of 15xc2x0 to 17xc2x0
at n 1.95 and UHFW of 42xc2x0angles of 11xc2x0 to 14xc2x0
at n 1.95 and UHFW of 43xc2x0angles of 6xc2x0 to 12xc2x0
at n 1.95 and UHFW of 44xc2x0angles of 2xc2x0 to 9xc2x0
at n 1.95 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 1.95 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.00 and UHFW of 41xc2x0angles of 15xc2x0 to 17xc2x0
at n 2.00 and UHFW of 42xc2x0angles of 10xc2x0 to 14xc2x0
at n 2.00 and UHFW of 43xc2x0angles of 6xc2x0 to 12xc2x0
at n 2.00 and UHFW of 44xc2x0angles of 2xc2x0 to 9xc2x0
at n 2.00 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.00 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.05 and UHFW of 41xc2x0angles of 15xc2x0 to 17xc2x0
at n 2.05 and UHFW of 42xc2x0angles of 10xc2x0 to 14xc2x0
at n 2.05 and UHFW of 43xc2x0angles of 6xc2x0 to 11xc2x0
at n 2.05 and UHFW of 44xc2x0angles of 2xc2x0 to 9xc2x0
at n 2.05 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.05 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.10 and UHFW of 41xc2x0angles of 14xc2x0 to 16xc2x0
at n 2.10 and UHFW of 41xc2x0angles of 10xc2x0 to 14xc2x0
at n 2.10 and UHFW of 43xc2x0angles of 6xc2x0 to 11xc2x0
at n 2.10 and UHFW of 44xc2x0angles of 2xc2x0 to 9xc2x0
at n 2.10 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.10 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.15 and UHFW of 41xc2x0angles of 14xc2x0 to 16xc2x0
at n 2.15 and UHFW of 42xc2x0angles of 10xc2x0 to 13xc2x0
at n 2.15 and UHFW of 43xc2x0angles of 5xc2x0 to 11xc2x0
at n 2.15 and UHFW of 44xc2x0angles of 2xc2x0 to 9xc2x0
at n 2.15 and UHFW of 45xc2x0angles of 0xc2x0 to 6xc2x0
at n 2.15 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.20 and UHFW of 46xc2x0angles of 14xc2x0 to 15xc2x0
at n 2.20 and UHFW of 42xc2x0angles of 10xc2x0 to 13xc2x0
at n 2.20 and UHFW of 43xc2x0angles of 5xc2x0 to 11xc2x0
at n 2.20 and UHFW of 44xc2x0angles of 2xc2x0 to 8xc2x0
at n 2.20 and UHFW of 45xc2x0angles of 0xc2x0 to 5xc2x0
at n 2.20 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.25 and UHFW of 41xc2x0angles of 14xc2x0 to 15xc2x0
at n 2.25 and UHFW of 42xc2x0angles of 10xc2x0 to 13xc2x0
at n 2.25 and UHFW of 43xc2x0angles of 5xc2x0 to 11xc2x0
at n 2.25 and UHFW of 44xc2x0angles of 2xc2x0 to 8xc2x0
at n 2.25 and UHFW of 45xc2x0angles of 0xc2x0 to 5xc2x0
at n 2.25 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.30 and UHFW of 41xc2x0angles of 14xc2x0 to 15xc2x0
at n 2.30 and UHFW of 42xc2x0angles of 9xc2x0 to 13xc2x0
at n 2.30 and UHFW of 43xc2x0angles of 5xc2x0 to 10xc2x0
at n 2.30 and UHFW of 44xc2x0angles of 2xc2x0 to 8xc2x0
at n 2.30 and UHFW of 45xc2x0angles of 0xc2x0 to 5xc2x0
at n 2.30 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.35 and UHFW of 41xc2x0angles of 13xc2x0 to 15xc2x0
at n 2.35 and UHFW of 42xc2x0angles of 9xc2x0 to 12xc2x0
at n 2.35 and UHFW of 43xc2x0angles of 5xc2x0 to 10xc2x0
at n 2.35 and UHFW of 44xc2x0angles of 2xc2x0 to 7xc2x0
at n 2.35 and UHFW of 45xc2x0angles of 0xc2x0 to 5xc2x0
at n 2.35 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.40 and UHFW of 41xc2x0angles of 13xc2x0 to 14xc2x0
at n 2.40 and UHFW of 42xc2x0angles of 9xc2x0 to 12xc2x0
at n 2.40 and UHFW of 43xc2x0angles of 5xc2x0 to 9xc2x0
at n 2.40 and UHFW of 44xc2x0angles of 2xc2x0 to 7xc2x0
at n 2.40 and UHFW of 45xc2x0angles of 0xc2x0 to 4xc2x0
at n 2.40 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.45 and UHFW of 41xc2x0angles of 13xc2x0 to 14xc2x0
at n 2.45 and UHFW of 42xc2x0angles of 9xc2x0 to 11xc2x0
at n 2.45 and UHFW of 43xc2x0angles of 5xc2x0 to 9xc2x0
at n 2.45 and UHFW of 44xc2x0angles of 2xc2x0 to 7xc2x0
at n 2.45 and UHFW of 45xc2x0angles of 0xc2x0 to 4xc2x0
at n 2.45 and UHFW of 46xc2x0angles of 0xc2x0
at n 2.50 and UHFW of 41xc2x0angles of 13xc2x0
at n 2.50 and UHFW of 42xc2x0angles of 9xc2x0 to 11xc2x0
at n 2.50 and UHFW of 43xc2x0angles of 5xc2x0 to 9xc2x0
at n 2.50 and UHFW of 44xc2x0angles of 2xc2x0 to 7xc2x0
at n 2.50 and UHFW of 45xc2x0angles of 0xc2x0 to 4xc2x0
at n 2.55 and UHFW of 41xc2x0angles of 13xc2x0
at n 2.55 and UHFW of 42xc2x0angles of 9xc2x0 to 11xc2x0
at n 2.55 and UHFW of 43xc2x0angles of 5xc2x0 to 9xc2x0
at n 2.55 and UHFW of 44xc2x0angles of 2xc2x0 to 7xc2x0
at n 2.55 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.60 and UHFW of 41xc2x0angles of 13xc2x0
at n 2.60 and UHFW of 42xc2x0angles of 9xc2x0 to 11xc2x0
at n 2.60 and UHFW of 43xc2x0angles of 5xc2x0 to 9xc2x0
at n 2.60 and UHFW of 44xc2x0angles of 2xc2x0 to 7xc2x0
at n 2.60 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.65 and UHFW of 42xc2x0angles of 9xc2x0 to 11xc2x0
at n 2.65 and UHFW of 43xc2x0angles of 5xc2x0 to 9xc2x0
at n 2.65 and UHFW of 44xc2x0angles of 2xc2x0 to 6xc2x0
at n 2.65 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.70 and UHFW of 42xc2x0angles of 9xc2x0 to 10xc2x0
at n 2.70 and UHFW of 43xc2x0angles of 5xc2x0 to 9xc2x0
at n 2.70 and UHFW of 44xc2x0angles of 2xc2x0 to 6xc2x0
at n 2.70 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.75 and UHFW of 42xc2x0angles of 9xc2x0 to 10xc2x0
at n 2.75 and UHFW of 43xc2x0angles of 5xc2x0 to 8xc2x0
at n 2.75 and UHFW of 44xc2x0angles of 2xc2x0 to 6xc2x0
at n 2.75 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.80 and UHFW of 42xc2x0angles of 9xc2x0 to 10xc2x0
at n 2.80 and UHFW of 43xc2x0angles of 5xc2x0 to 8xc2x0
at n 2.80 and UHFW of 44xc2x0angles of 2xc2x0 to 6xc2x0
at n 2.80 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.85 and UHFW of 42xc2x0angles of 9xc2x0
at n 2.85 and UHFW of 43xc2x0angles of 5xc2x0 to 8xc2x0
at n 2.85 and UHFW of 44xc2x0angles of 2xc2x0 to 6xc2x0
at n 2.85 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.90 and UHFW of 42xc2x0angles of 9xc2x0
at n 2.90 and UHFW of 43xc2x0angles of 5xc2x0 to 8xc2x0
at n 2.90 and UHFW of 44xc2x0angles of 2xc2x0 to 6xc2x0
at n 2.90 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 2.95 and UHFW of 42xc2x0angles of 8xc2x0 to 9xc2x0
at n 2.95 and UHFW of 43xc2x0angles of 5xc2x0 to 8xc2x0
at n 2.95 and UHFW of 44xc2x0angles of 2xc2x0 to 6xc2x0
at n 2.95 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
at n 3.00 and UHFW of 42xc2x0angles of 8xc2x0 to 9xc2x0
at n 3.00 and UHFW of 43xc2x0angles of 5xc2x0 to 8xc2x0
at n 3.00 and UHFW of 44xc2x0angles of 2xc2x0 to 6xc2x0
at n 3.00 and UHFW of 45xc2x0angles of 0xc2x0 to 3xc2x0
Principal crown facet angles (OHFW) for values of n and principal pavilion facet angles (UHFW) not specifically specified above may be interpolated from the above specified values.
According to additional embodiments the cut gem may further include a number of principal crown facets, the stone having a table of a diameter which preferably amounts to 0 to 85% of the diameter of the girdle surface.
For a diamond, the group of preferred principal crown facet angles (OHFW) according to an embodiment of the present invention comprises the following angles:
with UHFW of 41xc2x0angles of 11xc2x0 to
with UHFW of 42xc2x0angles of 7xc2x0 to 14xc2x0
with UHFW of 43xc2x0angles of 4xc2x0 to 12xc2x0
with UHFW of 44xc2x0angles of 1xc2x0 to 10xc2x0
with UHFW of 45xc2x0angles of 0xc2x0 to 7xc2x0
with UHFW of 46xc2x0angles of 0xc2x0 to 3xc2x0
According to another embodiment of the invention, within the group of preferred angles from which the principal crown facet angle is selected is a group of especially preferred principal crown facet angles (OHFW) which comprises the following angles:
with UHFW of 41xc2x0angles of 13xc2x0 to 14xc2x0
with UHFW of 42xc2x0angles of 9xc2x0 to 12xc2x0
with UHFW of 43xc2x0angles of 5xc2x0 to 9xc2x0
with UHFW of 44xc2x0angles of 2xc2x0 to 7xc2x0
with UHFW of 45xc2x0angles of 0xc2x0 to 4xc2x0
with UHFW of 46xc2x0angles of 0xc2x0
The raw material used for cutting the cut gem may be either a natural stone or synthetic material.
In addition to principal pavilion facets (UHFW) and principal crown facets (OHFW), the gem stone may include additional dependent pavilion facets and/or dependent crown facets. According to such embodiment, the principal crown facets may have an angle selected from the group of especially preferred principal crown facet angles (OHFW) and the dependent crown facets may have an angle selected from the group of preferred angles.
The number of pavilion facets and/or and the number of crown facets may be an even or an odd number. According to one preferred embodiment, the number of pavilion facets and/or the number of crown facets is greater than 13.
Furthermore the edges between the principal pavilion facets and the principal crown facets may be mutually offset on the girdle surface. The girdle surface may be of any shape, and may be either formed as an edge between the pavilion facets and the crown facets, or consist of one or several rounded or flat facets of any height. The gem stone according to the invention may be either manually or automatically cut.
By systematic cutting trials and by systematically calculating the reflection (light efficiency) as a function of the preselected cut angle, while simulating various lighting conditions, it has been established that optimal reflection may only be realized within a narrow range of 41xc2x0 to 46xc2x0 of the lower part (pavilion) principal facet angle. As a function of a lower part (pavilion) principal facet angle, and of a mean optical refraction of the raw material to be cut between n 1.50 and 3.00, a relatively limited number of angles resulting in a high degree of reflection for the cut gems is produced for the upper part (crown) principal facets. This angle range is described as the preferred angle range. The greatest light efficiency results from a generally smaller range of especially preferred angles.
A high-reflection gem cut can therefore be determined for an available natural or synthetic uncut gem, so as to result in optimal utilization of the existing raw material. Determining the cut may be done without further technical auxiliary materials, simply by following the specified technical theory. However, it is also possible to determine for the available uncut gem a computer-controlled cut of optimal light efficiency. Thus, the dimensions of an uncut gem, for example, can be optically measured by an already known computer-controlled system. Adjusting a cut to the required dimensions is also part of the state of the art. If, on the basis of the invention, the preferred or especially preferred angle combination and the light refraction of the material to be processed are entered into the computer program of the automatic machine, it becomes automatically possible to achieve a high reflection cut and optimal material utilization (weight).
Cutting the gem with the values determined in this way may be implemented manually or automatically, and even without further manual handling of the stone after it was optically measured. According to the present state of the art, such automatic measuring and cutting machines are commercially available.
With natural raw material, a finished gem with facets may naturally only be obtained by a cutting procedure. For synthetic material, such as glass, additional alternatives are available, such as molding, pressing forming, etc., which are considered equivalent to the cutting a procedure applicable to natural material.
If, in the aforementioned system, high light efficiency occurs when a group of upper part (crown) principal facet angles enclose an angle of 0xc2x0, then instead of a minimum of three principal crown facets at an angle of 0xc2x0, one table is produced. Thus, practically speaking, at an angle of 0xc2x0 several principal crown facets merge into one table. If the principal crown facet angle differs from 0xc2x0, then an additional table may be present. Supplementary to the principal crown facets and the principal pavilion facets, additional dependent facets may exist, resulting in especially high light efficiency when the principal crown facets are within the range of especially preferred angles, and the dependent crown facets are within the range of preferred angles.
Gems can be cut with an even and/or odd number of principal crown facets or principal pavilion facets, whereby the number of principal crown facets is equal to, or differs from the number of principal pavilion facets. An especially high light efficiency results from any even or odd number of facets which is greater than 13.
The edges of the principal crown facets and those of the principal pavilion facets may abut on the girdle surface; the surfaces, however, may also be mutually offset.
The girdle surface may have any shape and may, for example, be round, oval, square, or rectangular. The girdle may be made in the form of an edge located between the facets of the pavilion and the facets of the crown; however, it also may consist of one or more rounded or flat surfaces of any chosen height.
In case of cuts with several crown facets and/or a few pavilion facets, usually the principal facets are larger than the various dependent facets. Additional examples and definitions can be derived from the embodiment examples.